In geometry, the Poincaré disk model, also called the conformal disk model, is a model of 2-dimensional hyperbolic geometry in which all points are inside...

convenient to use the Poincaré disk model or the Poincaré half-plane model. Both the Poincaré disk model and the Klein disk model are models of the hyperbolic...

One is the Poincaré half-plane model, defining a model of hyperbolic space on the upper half-plane. The Poincaré disk model defines a model for hyperbolic...

half-plane model is named after Henri Poincaré, but it originated with Eugenio Beltrami who used it, along with the Klein model and the Poincaré disk model, to...

absolute of the Poincaré disk model and the Klein disk model. The real line forms the Cayley absolute of the Poincaré half-plane model. Pasch's axiom and...

point in S+ analogous to the gnomonic projection of the sphere; the Poincaré disk model is a projection of S+ through a point on the other sheet S− onto...

There are four models commonly used for hyperbolic geometry: the Klein model, the Poincaré disk model, the Poincaré half-plane model, and the Lorentz...

horocycles where the horocycles are a distance 1 apart is e : 1. In the Poincaré disk model of the hyperbolic plane, horocycles are represented by circles tangent...

Problems Generalized Poincaré conjecture Poincaré disk model, a model of hyperbolic geometry Poincaré duality Twisted Poincaré duality Poincaré–Einstein synchronization...

common models of hyperbolic geometry: the Poincaré half-plane model where the absolute is the real line on the complex plane, and the Poincaré disk model where...

Poincaré model can refer to: Poincaré disk model, a model of n-dimensional hyperbolic geometry Poincaré half-plane model, a model of two-dimensional hyperbolic...

A proof is in "Wilson Stothers' Cabri Pages". Tilings of the Poincaré disk model of the Hyperbolic plane exist having Saccheri quadrilaterals as fundamental...

Poincaré half-plane model by the mapping g given above. Both the Poincaré disk and the Poincaré half-plane are conformal models of the hyperbolic plane...

{\displaystyle ds={\frac {|dz|}{\operatorname {Im} (z)}}} and in the Poincaré disk model to d s = 2 | d z | 1 − | z | 2 {\displaystyle ds={\frac {2|dz|}{1-|z|^{2}}}}...

manifold Poincaré duality Poincaré disk model Poincaré expansion Poincaré gauge Poincaré group Poincaré half-plane model Poincaré homology sphere Poincaré inequality...

three-dimensional cartesian coordinates. This is the spherical analog of the Poincaré disk model of the hyperbolic plane. Intuitively, the stereographic projection...

model, the angles at the vertices of an ideal triangle are not zero, because the Beltrami-Klein model, unlike the Poincaré disk and half-plane models...

intersect with the axis d using the formula l = d cosh r. In the Poincaré disk model of the hyperbolic plane, hypercycles are represented by lines and...

Weisstein, Eric W. "Hyperbolic tiling". MathWorld. Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld. Hyperbolic and Spherical Tiling Gallery Archived 2013-03-24...

Weisstein, Eric W. "Hyperbolic tiling". MathWorld. Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld. Hyperbolic and Spherical Tiling Gallery Archived 2013-03-24...

models for the hyperbolic plane are the Poincaré disk model and Poincaré half-plane model. In these, the points of the hyperbolic plane are modeled by...

Weisstein, Eric W. "Hyperbolic tiling". MathWorld. Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld. Hyperbolic and Spherical Tiling Gallery KaleidoTile...

4, 6, and 14 triangles meeting at each vertex. The image shows a Poincaré disk model projection of the hyperbolic plane. It is labeled V4.6.14 because...

is circumscribed by a horocycle, which looks like a circle in a Poincaré disk model, internally tangent to the projective circle boundary. The edges...

Weisstein, Eric W. "Hyperbolic tiling". MathWorld. Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld. Hyperbolic and Spherical Tiling Gallery KaleidoTile...

hyperbolic tree commonly utilizes the Poincaré disk model of hyperbolic geometry, though the Klein-Beltrami model can also be used. Both display the entire...

In the conformal ball model, a horosphere is represented by a sphere tangent to the horizon sphere. In the upper half-space model, a horosphere can appear...

y_{b}=\tanh(y_{a})} The Poincaré coordinates of a point are the Cartesian coordinates of the point when the point is mapped in the Poincaré disk model of the hyperbolic...

space thus defines the required biholomorphism. This model is the equivalent of the Poincaré disk model. Unlike the real hyperbolic space, the complex projective...

Weisstein, Eric W. "Hyperbolic tiling". MathWorld. Weisstein, Eric W. "Poincaré hyperbolic disk". MathWorld. Hyperbolic and Spherical Tiling Gallery KaleidoTile...